System and method for automated machining of toothed members

ABSTRACT

A method for machining a workpiece to provide a toothed member having a desired tooth pattern. The workpiece is machined to a first depth using a cutting tool, thereby forming a semi-finished tooth pattern, the first depth less than a full depth to which the workpiece is to be machined to provide the desired tooth pattern. Dimensions of the semi-finished tooth pattern are acquired and compared to nominal dimensions. If the acquired dimensions are not within a tolerance of the nominal dimensions, the geometry of the cutting tool is modified for correcting deviations of the acquired dimensions from tolerance and the workpiece further machined by the modified cutting tool. Once the dimensions of the semi-finished tooth pattern are within tolerance, the workpiece is machined to the full depth for providing the desired tooth pattern.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a Continuation of U.S. patent applicationSer. No. 14/573,899 filed on Dec. 17, 2014, the contents of which arehereby incorporated by reference.

TECHNICAL FIELD

The disclosure relates generally to automated machining of parts and,more particularly, toothed members.

BACKGROUND OF THE ART

Toothed members, such as curvic couplings, are commonly found in gasturbine engines as they provide connection between engine parts andpermit highly precise centering and stacking of engine parts. Given thetight tolerances required for aerospace applications, such toothedmembers have to be machined with great accuracy in order to ensureproper functioning in the engine. Therefore, machine tool operators aretypically required to make several manual interventions during themachining process in order to ensure that parameters (e.g.concentricity, perpendicularity, addendum, pitch plane height, contactpattern) associated with a freshly machined toothed member are withinrequired specifications.

In particular, as part of the conventional manufacturing process, anoperator is typically required to use a master gauge, depth micrometer,and height gauge at various stages of the machining process to ensurethat the dimensions of the freshly machined part are within tolerance.Given the complexity of the manufacturing process, a substantial amountof manual measurement and setup operations is required, which provestime consuming and costly.

There is therefore a need for improved systems and methods formanufacturing parts, such as toothed members, that are subject to tighttolerances.

SUMMARY

In one aspect, there is provided a method for machining from a workpiecea toothed member with a desired tooth pattern. The method comprisesmachining the workpiece to a predetermined partial depth using a cuttingtool to provide a semi-finished tooth pattern created according to ageometry of the cutting tool, the predetermined partial depth less thana full depth of the desired tooth pattern; comparing computed parametersof the semi-finished tooth pattern based on dimensions of thesemi-finished tooth pattern to nominal parameters of the semi-finishedtooth pattern and determining whether the computed parameters are withina predetermined tolerance of the nominal dimensions for thesemi-finished tooth pattern at the predetermined partial depth;modifying the geometry of the cutting tool to correct deviations of thecomputed parameters from the tolerance when the computed parameters arenot within the predetermined tolerance of the nominal dimensions, andmachining the workpiece with the modified cutting tool to bring thedimensions of the semi-finished tooth pattern within the tolerance forthe semi-finished tooth pattern at the predetermined partial depth; andmachining the workpiece to the full depth to provide the desired toothpattern when the dimensions of the semi-finished tooth pattern arewithin the tolerance for the semi-finished tooth pattern at thepredetermined partial depth.

DESCRIPTION OF THE DRAWINGS

Reference is now made to the accompanying figures in which:

FIG. 1 is a schematic cross-sectional view of a gas turbine engine;

FIG. 2 is a flowchart of a method for manufacturing a toothed member, inaccordance with an illustrative embodiment;

FIG. 3 is a flowchart of the step of FIG. 2 of probing and adjusting aworkpiece and fixture setup;

FIG. 4 is a flowchart of the step of FIG. 2 of adjusting cutting toolparameters and subjecting the cutting tool to an initial dressingoperation;

FIG. 5 is a flowchart of the step of FIG. 2 of automated machining ofthe workpiece;

FIG. 6a is a perspective view of a cutting tool machining a workpiece,in accordance with an illustrative embodiment;

FIG. 6b is a perspective view of the workpiece of FIG. 6a being machinedto form a toothed member;

FIG. 6c is a schematic diagram showing the tooth form of a toothedmember, in accordance with an illustrative embodiment;

FIG. 6d is a schematic diagram showing the profile of a convex cuttingtool, in accordance with an illustrative embodiment;

FIG. 6e is a schematic diagram showing the profile of a concave cuttingtool, in accordance with an illustrative embodiment;

FIG. 7 is a flowchart of the step of FIG. 5 of correlating parameterscomputed for a semi-finished workpiece to master gauge parameters;

FIG. 8 illustrates a master gauge under analysis on a scanningcoordinate measuring machine (CMM) and reconstructed surfaces of themaster gauge teeth from the CMM inspection, in accordance with oneembodiment;

FIG. 9 is a schematic diagram showing dressing of a cutting tool, inaccordance with one embodiment;

FIG. 10a and FIG. 10b are schematic diagrams showing redressing of aconvex cutting tool profile, in accordance with one embodiment;

FIG. 10c and FIG. 10d are schematic diagrams showing redressing of aconcave cutting tool profile, in accordance with one embodiment;

FIG. 11 is a flowchart of the step of FIG. 5 of further machining thesemi-finished surface to achieve at the desired toothed member geometry;

FIG. 12 is a schematic diagram of a system for machining a toothedmember, in accordance with one embodiment; and

FIG. 13 is a schematic diagram of an application running on theprocessor of FIG. 12.

DETAILED DESCRIPTION

FIG. 1 illustrates a gas turbine engine 10 of a type preferably providedfor use in subsonic flight, generally comprising in serial flowcommunication a fan 12 through which ambient air is propelled, acompressor section 14 for pressurizing the air, a combustor 16 in whichthe compressed air is mixed with fuel and ignited for generating anannular stream of hot combustion gases, and a turbine section 18 forextracting energy from the combustion gases. High pressure rotor(s) 20of the turbine section 18 are drivingly engaged to high pressurerotor(s) 22 of the compressor section 14 through a high pressure shaft24. Low pressure rotor(s) 26 of the turbine section 18 are drivinglyengaged to the fan rotor 12 and to other low pressure rotor(s) (notshown) of the compressor section 14 through a low pressure shaft 28extending within the high pressure shaft 24 and rotating independentlytherefrom.

The engine 10 illustratively comprises various parts, such as toothedmembers, that are to be machined with tight tolerances. The parts may bemachined using multi-axis Numerical Control (NC) (e.g. ComputerNumerical Control (CNC)) machining centers. A cutting tool provided onthe NC machine may be used to perform the machining operation. In oneembodiment, the machining operation comprises a grinding process, e.g.plunge grinding, and the cutting tool is a grinding wheel (e.g.cup-shaped). Still, it should be understood that other suitablemachining processes and accordingly other cutting tools, may apply.

Referring to FIG. 2, a method 100 for manufacturing a toothed memberwill now be described. In one embodiment, the method 100 is used tomanufacture a curvic coupling, i.e. a toothed connection member that canbe used to transmit torque between rotating elements. Curvic couplingsare commonly found in gas turbine engines, such as the engine 10 of FIG.1, for several reasons. First, curvic couplings can be machined directlyonto rotors such as axial and centrifugal compressors and turbine disks,eliminating the need for separate shafts. Rotors can then be stackedclosely and accurately with minimal distance between mating parts.Second, curvic couplings permit highly precise centering of parts duringdisassembly and installation in an engine. In addition, curvic couplingsare relatively quick to manufacture if a suitable machine and cuttingtool are available. It should however be understood that, although theproposed system and method are presented herein as being used tomanufacture curvic couplings, other toothed members, including, but notlimited to, splines, gears (e.g. bevel gears and spur gears), couplingsand slots, may apply.

A curvic coupling typically has teeth spaced circumferentially about itsface, the teeth having a curved shape when viewed in a planeperpendicular to a central (or “coupling”) axis of the curvic couplingand the two opposed sides of a given tooth in a curvic coupling beingcurved in opposite directions. Two mating curvic couplings are typicallycoupled to create a connection, with one curvic coupling being made withconvex, or “barrel-shaped”, teeth while its mate is made with concave,or “hour-glass-shaped”, teeth. Curvic coupling teeth can be producedwith a wide range of pressure angles to suit various applications. Allteeth of a given curvic coupling are generally ground to a constantdepth and a theoretical radius, which have to be accurate withinprescribed tolerances in order to ensure proper engagement with matingcurvic couplings.

The method 100 illustratively comprises installing at step 102 into afixture, e.g. a fixture with a zero-point clamping system, a workpiece(e.g. an annular-shaped workpiece) to be machined to obtain a desiredtoothed member (e.g. curvic coupling or gear). It is desirable forlocating face(s) on the workpiece and fixture to be manufactured suchthat tolerances on flatness for the workpiece and fixture aresignificantly below those of the finished toothed member obtainedpost-machining. The next step 104 is then to load the workpiece andfixture assembly into an NC machine (e.g. an NC grinding machine). Thismay be achieved using an automated loading/unloading system, such as arobot with a quick change zero-point clamping system. Alternatively,loading may be performed by an operator. In one embodiment, once thefixture is placed into a loading position on a work table of the NCmachine, a signal will be sent by the NC machine to cause clamping orunclamping of the fixture into position on the work table.

The setup obtained at step 104 may then be probed and adjusted as neededat step 106. Referring to FIG. 3, the step 106 of probing and adjustingthe workpiece and fixture setup illustratively comprises probing at step202 the initial position of a circular reference datum to verify theparallelism of the workpiece with a locating face of the fixture. Asused herein, the term “datum” refers to one or more reference points orsurface(s) that measurements are taken from. The circular referencedatum may have been predetermined and defined on the engineeringdrawings or manufacturing operation sheet. In one embodiment, the datumused for measuring parallelism is the face on the workpiece where thetoothed member is ground. However, it should be understood that thedatum could also be two or more diameter locations near the area of theannular-shaped toothed member. The probing may be performed at step 202using a part probing system (e.g. a scanning or touch probing system)provided on (e.g. integrated with) the NC machine. In order to acquiremeasurements, a tip of a probe may be moved along a pre-programmed (e.g.NC programmed) probing direction toward positions on the workpiece wheremeasurements are to be acquired. The probe may further be coupled to aforce sensor (not shown), which acquires a measurement signal when theprobe tip touches the surface of the workpiece. In one embodiment, theprobing system is a strain-gage. It should be understood that otherprobing systems or measuring devices may apply. For example, acoordinate measuring machine (CMM) connected to the NC machining centermay be used to acquire measurements on a surface of the workpiece.

A measure of the parallelism of the workpiece relative to the fixturemay be obtained from the acquired measurements. This may be achieved byprobing several points on the face of the workpiece where the toothedmember is ground and computing the difference between the minimum andmaximum height values (e.g. z-values). Alternatively, a plane may befitted through a number of (e.g. three (3)) probed points and the heightdifference at the extremes of the plane (at the diameters of the toothedmember area) may then be computed. Multiple points may also be probedand a plane calculated by a least-squares or regression plane fittingalgorithm. In other embodiments, the measure of the parallelism may beobtained by finding the center of two or more diameter locations, onebeing at the toothed member face, and fitting a plane whose normal is aline connecting the two (or more) diameters. If the workpiece is notparallel with the fixture's locating face and a deviation is measured,the next step 204 may then be to assess whether the deviation fromparallelism is within a predetermined tolerance. Tolerances referred toherein are illustratively defined by engineering drawings ormanufacturing operation sheets. Typical values are between 0.0002 and0.002 inches. If this is not the case, i.e. the deviation is beyondtolerance, the next step 206 may be to cause realignment of theworkpiece by generate an alarm accordingly. Alternatively, themisalignment may be corrected at step 206 by implementing acontroller-based compensation method, provided such an option isavailable on the NC machine and the latter has an appropriate number ofaxes for implementation of the compensation method. In one embodiment,at least five (5) axes are used for parallelism compensation, comprisingthree (3) linear axes and two (2) rotary axes. The method may then flowback to repeat steps 202 and 204.

When it is determined at step 204 that the deviation from parallelism iswithin tolerance, concentricity of the workpiece relative to a rotaryaxis of the NC machine's work table may then be checked. For thispurpose, a series of points may be probed on the workpiece datum and acircle fitted through the points at step 208. A face is illustrativelyused as a datum to measure parallelism, as discussed above, while adiameter is used as a datum to measure concentricity. However, it shouldbe understood that it is possible to use two (2) or more diameters (e.g.a cylinder) as a datum for the parallelism measurement with one of thesediameters being coincident with the same diameter used to measureconcentricity. The more points probed at step 208, the higher the degreeof accuracy. The workpiece will be found to be concentric with therotary axis of the NC machine's work table if the rotary axis passesthrough the center of the circle fitted through the probed points. Ifthe workpiece is not concentric with the work table, it may be assessedat step 210 whether the deviation from concentricity is within apredetermined tolerance. Typical tolerances for concentricity of toothedmembers (e.g. curvic couplings) are between 0.0002 and 0.002 inches. Ifthis is not the case, the location of the center of the fitted circle isshifted as needed at step 212 to bring the concentricity withintolerance. In one embodiment, only two (2) linear axes (typically X andY axes) are needed to compensate for an out-of-concentricity condition.Such shifting may be performed manually, using a robot, or by acontroller-based compensation method if available. The method may thenflow back to repeat steps 208 and 210. When it is determined at step 210that the concentricity is within tolerance, the method proceeds with thestep 108 of FIG. 2 of adjusting the cutting tool parameters as neededand subjecting the cutting tool to an initial dressing operation.

It should be understood that the concentricity may be verified prior toverifying the parallelism of the workpiece and the order of steps 202 to212 may be changed accordingly. It should also be understood that steps204 and 210 may not be performed if it is already determined from theacquired measurements (e.g. at steps 202 and 208) that no deviation fromparallelism or concentricity exists.

Referring now to FIG. 4 in addition to FIG. 2, the step 108 of adjustingthe cutting tool parameters as needed and subjecting the cutting tool toan initial dressing operation illustratively comprises calling thecutting tool to the NC machine's spindle (e.g. the NC machine's mainshaft) from an automatic tool changing (ATC) system on the NC machine.In some embodiments, the NC machine may indeed store a plurality oftools in a tool magazine, with each tool being called (e.g. brought) tothe spindle (e.g. by the ATC) when the tool is to be used. Some NCmachines further have automatic nozzle changing capability, with eachcutting tool having a dedicated coolant manifold to optimally cool andflush the grinding zone. This eliminates the need for an operator toinstall and align nozzles in the setup. The next step 304 may then be toprobe the cutting tool with a suitable measuring device (e.g. laser ortouch tool probing system) to obtain an estimate of the true (or real)diameter and axial thickness of the cutting tool. The estimated diameterand axial thickness may then be compared to nominal dimensions and itmay be determined at step 308 whether offsets (i.e. radial and/or axial)from the nominal dimensions exist. It may be desirable for the cuttingtool to be wide enough to cover at least half of the width of a spacebetween two adjacent teeth formed on the workpiece, yet narrow enough topass through the tooth space (or tooth slot) during machining.

As used herein, the term “nominal” as applied to a part, surface,geometrical element, etc., is intended to refer to the part, surface,geometrical element (e.g. a surface, profile, angle, plate, or otherfeature defining the part), etc., as defined in a theoretical model suchas a Computer Aided Design (CAD) model or other digitally stored orrecreated model, without tolerance, which may be used as a referencewhen machining one or a plurality of similar actual parts, surfaces,geometrical elements, etc. The term “real”, “actual”, or “true” asapplied to a part, surface, geometrical element, etc., is intended torefer to the real, physical part, surface, geometrical element, etc., atvarious stages of the manufacturing process, including any variationbrought by that process.

If it is determined at step 308 that radial and/or axial offsets fromnominal dimensions exist, the one or more offsets are sent at step 310to the NC machine controller to cause adjustment of the cutting tool'sthickness and diameter compensation in an NC dressing program for thecutting tool. If it was determined at step 308 that no offsets exist orafter step 310 has been performed, the cutting tool is subjected at step312 to an initial dressing operation in accordance with the NC dressingprogram.

In one embodiment, the cutting tool is a dressable cup-shaped grindingwheel that may be dressed by the use of a dressing tool, such as a wheelor grinding dresser. In one embodiment, the dressing tool is a rotarydresser, e.g. a disc with a hard material, such as diamond, attached tothe edge. It should however be understood that other types of dressingtools, e.g. stationary dressing tools, may apply. It should also beunderstood that, although toothed members, such as curvic couplings, maybe ground using plated grinding wheels, where the tooth form ismanufactured onto the wheel, it is preferable to use dressable wheels toensure on-machine adjustment of the shape of the toothed member, as willbe discussed further below. As used herein, the term dressing refers toan operation of removing a current layer of abrasive material on thecutting tool so as to modify a profile of the cutting tool. The abrasivematerial includes, but is not limited to, aluminum oxide, siliconcarbide, and vitrified cubic boron nitride (CBN), with each abrasivegrain serving as a small cutting element. Selection of the abrasivematerial illustratively depends on cost, required tolerances, and partmaterial.

The NC dressing program is illustratively generated to move the face ofthe cutting tool (e.g. the grinding wheel) across the radius (or edge)of the dressing tool in order to create a desired profile for thecutting tool, the profile corresponding to a shape required by thedimensions of the toothed member to be machined. Indeed, the dressingoperation performed at step 312 in accordance with the NC dressingprogram illustratively modifies the profile (or geometry) of the cuttingtool so as to achieve in the cutting tool a profile that will create adesired tooth profile or pattern (e.g. as defined in a theoretical modelsuch as a CAD model) in the toothed member when the latter is machinedby the cutting tool. The dressing operation of step 312 may involveplunging the cutting tool, e.g. the grinding wheel, into a shaped rollof abrasive material. Alternatively, the required shape may be formed onthe grinding wheel by moving the latter over a radius on a single pointor rotary-type dresser in accordance with the NC dressing program. Thelatter technique may be preferable as it allows for the tooth profile tobe modified by adjusting the NC program for correcting errors owing tostackup of tolerances or misalignments in axes of the NC machine cuttingtool. In one embodiment, an acoustic emission sensor may be employed tofind the position where the cutting tool touches the dresser and toensure an even and complete dressing of the cutting tool. The NCdressing program may be fully parametric, e.g. equation-based, such thatthe dressing tool path and hence the shape of the cutting tool (e.g. thewheel shape) can be updated by changing parameters in the NC programfrom the probed dimensions (i.e. pressure angle and tooth width).

Referring back to FIG. 2, after the cutting tool has been initiallydressed at step 108, automated machining of the workpiece may beperformed at step 110, as will be discussed further below with referenceto FIG. 5. Step 110 illustratively comprises generating a machining(e.g. NC) program comprising commands that indicate anumerically-controlled tool path to be followed by at least the cuttingtool for machining the workpiece and manufacturing the toothed member.Similarly to the NC dressing program, the NC machining (e.g. grinding)program may be fully parametric, e.g. equation-based, such that themachining tool path is updated by changing parameters in the NC program.Post-machining, the machined workpiece (i.e. the finished toothedmember) may be inspected at step 112. Step 112 may comprise verifyingconcentricity, perpendicularity, and/or parallelism of the freshlymachined workpiece by probing. For this purpose, the automatedloading/unloading system (or the operator) removes the workpiece andfixture from the NC machine and the workpiece is sent to an inspectionstation at a remote location. In one embodiment, three (3) or more teethare probed on the machined workpiece to measure concentricity,perpendicularity, and parallelism of the tooth pattern. A contactpattern check typical for inspection of toothed members, such as curviccoupling, may also be performed on the machined workpiece. In oneembodiment, the contact pattern check may comprise application of a gearmarking compound on a master gauge, which may be a produced toothedmember having a geometry that is complementary (e.g. the mirror image)to that of the toothed member to be machined. The master gauge is thenseated on the freshly machined workpiece, tapped into place using asuitable tool (e.g. a hammer) and removed. The gear compound transferredto the teeth on the workpiece then indicates the manner in which themating teeth (i.e. the teeth of the master gauge and of the machinedworkpiece) contact each other. From the transfer pattern of the gearcompound, it can be determined if satisfactory contact is made betweenthe master gauge and the freshly machined workpiece. An acceptablecontact pattern may be defined by requirements such as a well-centeredshape, a given percentage of teeth in contact, and a limited number ofconsecutive teeth missing contact.

In the proposed automated machining process, an acceptable contactpattern may be ensured at step 112 by selecting a suitable abrasivematerial for the cutting tool. An acceptable contact pattern can also beensured by sufficiently dressing the cutting tool at step 108 to ensurethat the cutting tool's form does not break down during the machiningprocess and that any undesirable tooth profiles that may be found on theworkpiece are completely removed. In addition, the pressure angle, toothgeometry and machine offsets may be initially verified on a test ringwith the above-mentioned contact pattern check. Periodic measurementsand adjustments can be taken from time to time to reduce the possibilityof drift. Moreover, using a precise, well-aligned and well-maintainedmachine and ensuring the dressing tool is replaced at suitable intervalsto prevent excessive wear to machine the workpiece can achieve anacceptable contact pattern. Finally, keeping the NC machine and probingsystem accurate and well-aligned through frequent calibrations andadjustments (e.g. ball-bar checks) can also achieve an acceptablecontact pattern.

If the contact pattern is found to be unacceptable at step 112, the NCmachine and NC program may be recalibrated and adjusted. Acceptableresults may be confirmed by testing on representative test rings. Theworkpiece can then be returned to the NC machine for a rework cycle(i.e. for repeating steps 102 to 112). Removing a small amount ofmaterial by plunging into the workpiece with a correctly dressed cuttingtool will usually be sufficient to restore the workpiece surfaces to anacceptable contact pattern.

Referring now to FIG. 5, the step 110 of automated machining of theworkpiece illustratively comprises the step 402 of positioning thecutting tool over the workpiece at a desired location. At step 404, theworkpiece is exposed to the cutting tool, e.g. the cutting tool isplunged into the workpiece up to a predetermined partial depth, in orderto obtain a semi-finished surface comprising a plurality of rough toothslots. The partial depth is smaller than the desired full depth up towhich the workpiece is to be machined. In one embodiment, the partialdepth is in a range between 30% and 50% of the full depth. It should beunderstood that other ranges may apply so long as the partial depth thatis reached enables to measure parameters (e.g. dimensions) of thesemi-finished surface (as will be discussed further below) and allowsfor subsequent adjustments (e.g. further machining) to be performed onthe semi-finished surface, if needed.

The next step 406 may therefore be to assess whether the predeterminedpartial depth has been reached. If this is not the case, the workpiecemay be further machined by returning to step 404. Once the cutting toolhas machined the workpiece up to the partial depth as determined at step406, the next step may be to retract the cutting tool and assess at step410 whether more teeth need to be machined. If this is the case, therotary axis of the NC machine's work table may be indexed to the nextset of teeth to be machined and the method may flow back to step 404 forrepeating the machining process for the next set of teeth. The procedureis repeated until all teeth are ground in the workpiece up to therequired partial depth. It should be understood that, depending on therequirements, each tooth may be machined up to the partial depth inseveral steps. For example, in order to achieve a desired tooth tapertowards the center of the toothed member, the cutting tool may firstmachine half of each tooth slot and the workpiece rotated for machiningthe other half of the tooth slot. Also, due to the cutting tool'sannular shape and position (e.g. off-axis) over the workpiece, duringeach pass of the cutting tool, the half of a first tooth slot may bemachined concurrently to the half of a second tooth slot located apredetermined distance (e.g. eight (8) to ten (10) teeth) away from thefirst tooth slot. In this manner, teeth can be machined using an eventamount of material and balance can be achieved in the machining process.

Once it is determined at step 410 that the workpiece has been machinedsuch that all teeth have been ground up to the partial depth, the methodmay flow to the step 412 of probing the resulting semi-finished surface.The semi-finished surface may be probed using any suitable measuringdevice, such as an on-machine part probing system, scanning probe, touchprobe, or the like, as discussed above and step 412 may thereforecomprise instructing the measuring device to acquire the measurements(e.g. dimensions) of the workpiece. In one embodiment, locations on atop face and a bottom surface of the workpiece as well as two or morepoints on each pressure surface of one or more teeth of the workpieceare probed. Parameters (e.g. dimensions) of the machined workpiece maythen be computed on the basis the measurements acquired by probing. Inone embodiment where curvic couplings are being machined, the toothdepth, tooth width, and pressure angle are computed. It should beunderstood that in other embodiments, more or less parameters may becomputed. For example, an “X value” parameter, which is indicative of adistance from the center of the cutting tool to the center of theworkpiece, may be computed. Also, when the method described herein isused to manufacture a spline, different geometry may be measured andcalculated. It should also be understood that other dimensions of theworkpiece, including but not limited to surface finish, temperature, orthe like, may be acquired.

As will be discussed further below with reference to FIG. 7, at step414, the computed parameters may then be compared to theoreticalparameters, e.g. parameters obtained from a virtual tooth profile, suchas a scanned master gauge, the NC program adjusted, and the cutting toolsubjected to further dressing as needed. If the cutting tool isredressed, the workpiece is illustratively subjected to furthermachining by the redressed cutting tool at step 416 in order to bringthe parameters of the semi-finished surface within tolerance of thetheoretical parameters. After the workpiece is further machined, steps412 and 414 may be repeated until none of the parameters are found atstep 414 to be beyond tolerance. Once it is found that the parameters ofthe semi-finished surface are within tolerance of the theoreticalparameters, the semi-finished surface may be further machined at step418, i.e. the rough slots machined by the cutting tool up to the fulldepth, in order to achieve the desired toothed member geometry, as willbe discussed further below.

FIG. 6a illustrates a cutting tool, i.e. a grinding wheel 502, beingplunged into (e.g. along the direction of arrow A) an annular workpiece504 for grinding along a perimeter thereof a plurality of teeth as in506. In the illustrated embodiment, the workpiece is being machined toform a convex curvic coupling. It can be seen from the embodiment ofFIG. 6a that the grinding wheel 502 has an axis of rotation B and is notconcentric with the workpiece 504.

As can be seen in FIG. 6b , the teeth 506 machined in the workpiece 504,e.g. the curvic coupling, each have a root 508 and a pressure surface510. The tooth depth 512 can be measured as the overall height of eachtooth 506 as measured from the root 508 while the tooth thickness 514 isthe width of each tooth at the addendum (not shown). As can be seen inFIG. 6c , which illustrates the tooth form for a toothed member, such asthe curvic coupling 504 of FIG. 6b , each tooth 506 further has a givenpressure angle 516 that is measured as the angle between a tangent tothe tooth profile (i.e. a tangent to the pressure surface 510) and aline perpendicular to the pitch plane (or pitch surface) 518. Othergeometrical elements of the teeth 506 (e.g. the dedendum, addendum,gable, and the like) will be apparent to those skilled in the art.

Referring to FIG. 6d in addition to FIG. 6a , there is illustrated aprofile (not to scale) of the grinding wheel 502 for a convex curviccoupling, in accordance with one embodiment. It should be understoodthat various profiles other than the one illustrated in FIG. 6d mayapply. The grinding wheel's profile comprises, at an inner diameter (ID)of the wheel 502 (referred to “Wheel ID” in FIG. 6d ), an inner surface602, an outer surface 604 at an outer diameter (OD) of the wheel 502(referred to “Wheel OD” in FIG. 6d ), and a bottom face or edge,referred to as a gable 606. The gable 606 usually has a small angleϕ_(g) of zero (0) to five (5) degrees in order to eliminate the mismatchbetween the two sides of a tooth. If the gable angle is zero, a mismatchresults from the fact that for each tooth (e.g. machined using thegrinding wheel 502), one half is ground at one contact arc between thegrinding wheel 502 and the workpiece, while the other is ground at asecond arc. However, for a particular tooth, the two tooth halves areillustratively not ground simultaneously, as discussed above. As can beseen from FIG. 6a , the shape root plane (not shown) of the workpiece504 can be created by the gable 606 of the grinding wheel 502 while thepressure surfaces (reference 510 in FIG. 6b ) are shaped by the innerand/or outer surfaces 602, 604 respectively provided at an innerdiameter (ID) and an outer diameter (OD) of the wheel 502. Inparticular, the convex tooth profile of the machined curvic coupling maybe produced by the inner surface 602 of the grinding wheel 502 with thepressure surfaces 510 of the toothed member being created by a pressuresurface 608 provided at the wheel's inner surface 602. The pressureangle ϕ_(P) of the pressure surface 608 in turn defines the toothedmember's pressure angle (reference 516 in FIG. 6c ). Therefore, theprofile of the grinding wheel 502 determines the tooth profile createdin the machined toothed member and the cutting tool is dressedaccordingly to achieve a desired tooth profile.

FIG. 6e illustrates, in accordance with one embodiment, a profile of aconcave grinding wheel 502′ used to machine concave curvic couplingsthat match the convex curvic couplings machined using the grinding wheel502 of FIG. 6d . The grinding wheel 502′ comprises an inner surface 602′at the ID of the wheel 502′ (referred to “Wheel ID” in FIG. 6e ), anouter surface 604′ at the OD of the wheel 502′ (referred to “Wheel OD”in FIG. 6e ), and a gable 606′ having an angle ϕ_(g). The pressuresurfaces of a concave toothed member are created by a pressure surface608′ provided at the wheel's outer surface 604′. The pressure angleϕ_(P) of the pressure surface 608′ in turn defines the toothed member'spressure angle (reference 516 in FIG. 6c ). The concave profile of thewheel 502′ is illustratively a mirror image of the convex profile of thewheel 502 of FIG. 6d about an axis C, which is substantially parallel tothe tool axis B and centered at the wheel's pitch plane points(references 610 and 610′ in FIG. 6d and FIG. 6e ).

Referring now to FIG. 7, the step 414 of comparing the parameters (e.g.tooth depth, tooth width, and pressure angle) computed for thepartially-machined (i.e. semi-finished) workpiece to theoretical (ornominal) dimensions illustratively comprises correlating the computedparameters with theoretical parameters defined in a theoretical modelfor the toothed member to be machined. In one embodiment, thetheoretical parameters are obtained from a master gauge, which has beendesigned and produced to have the desired tooth profile to be achievedin the finished toothed member. It should however be understood that thetheoretical parameters may alternatively be obtained from a solid modelof a nominal part. Still, since machined parts are typically inspectedpost-machining using a master gauge, as discussed herein above, andsince mater gauges typically exhibit deviations from nominal partmodels, it is preferable to calibrate the probed toothed memberdimensions with respect to the master gauge. Step 414 thereforeillustratively comprises characterizing the master gauge to determineparameters thereof at step 702. This may involve scanning the mastergauge surfaces using a high precision measurement system. For example,as illustrated in FIG. 8, the master gauge 802 may be analyzed on ascanning CMM 804. Reconstructed surfaces 806 of the master gauge teethmay then be obtained from the CMM inspection and used to compute themaster gauge's dimensions. Alternatively, the master gauge parametersmay be determined at step 702 by installing the master gauge on themachined workpiece and inferring the master gauge dimensions throughmeasurement with manual gauging.

The tooth width and pressure angle computed at step 412 of FIG. 5 arethen compared at step 704 to the theoretical tooth width and pressureangle values obtained from characterization of the master gauge. Thismay be done by computing a difference or deviation between the computedand theoretical values. Once the computed pressure angle has beencompared to that determined form the master gauge, the method may assessat step 706 whether the computed pressure angle is beyond apredetermined tolerance of the theoretical pressure angle (e.g. obtainedfrom the master gauge measurements). The tolerance is illustrativelydefined by engineering drawings or manufacturing operation sheets. Inone embodiment, the tolerance is ±5 minutes of a degree. If this is notthe case (i.e. the computed pressure angle is not beyond a predeterminedtolerance of the theoretical pressure angle), the method may flow to thestep 418 of FIG. 5, i.e. further machine the semi-finished surface toachieve the desired toothed member geometry. Otherwise, if the computedpressure angle is beyond the tolerance, the NC dressing program isaccordingly adjusted at step 708 such that, upon the cutting tool beingredressed, the cutting tool's profile (e.g. the inner surface of thecutting tool) has a corrected pressure angle that in turn brings thepressure angle of the workpiece machined with the redressed cutting toolwithin tolerance. Indeed, since the workpiece's tooth pattern is createdby the cutting tool's geometry and the profile of the cutting toolaccordingly corresponds to the tooth pattern to be achieved, theworkpiece's pressure angle can be adjusted by modifying the cuttingtool's pressure angle.

At step 708, the cutting tool is thus subjected to a new dressingoperation according to the adjusted NC program, leading to a redressedcutting tool having a corrected form (i.e. a pressure angle withintolerance). It should be understood that when adjusting the pressureangle and redressing the cutting tool accordingly, it is desirable toensure that enough material is removed from the cutting tool so that theprevious pressure angle is completely removed from the cutting tool'sprofile and replaced with the new pressure angle. In one embodiment, dueto high sensitivity to pressure angle, the pressure angle need only bemodified slightly (e.g. by less than one (1) degree) in order to achievea desired correction. Also, rather than adjusting the pressure angle byredressing the cutting tool, the pressure angle may be adjusted bytilting (e.g. angling) the cutting tool relative to the axis B of FIG.6d . Still, redressing may be desirable in order to ensure fullautomation of the machining process and minimize human intervention. Thenext step 416 may then be to subject the workpiece to further machiningusing the redressed cutting tool, as discussed above with reference toFIG. 5. As a result of redressing the cutting tool, the pressure angleof the re-machined workpiece is brought within tolerance of the mastergauge pressure angle.

Once the computed tooth width has been compared to the tooth widthdetermined form the master gauge, the method may further assess at step710 whether the computed tooth width is beyond a predetermined toleranceof the theoretical (e.g. master gauge) tooth width. The tolerance isillustratively defined by engineering drawings or manufacturingoperation sheets. In one embodiment, the tolerance is ±0.0006 inches. Itshould however be understood that compliance of the tooth width withtolerances may be verified prior to verifying compliance of the pressureangle with tolerances and the order of steps 706 to 712 may be changedaccordingly. If it is determined at step 710 that the computed toothwidth is within tolerance, the method may flow to the step 418 of FIG.5, i.e. further machine the semi-finished surface to achieve the desiredtoothed member geometry. Otherwise, if the computed tooth width isbeyond the tolerance, the radial location of the cutting tool's profile(i.e. adjusting the radial distance between the cutting tool and thedressing tool) is automatically modified in the NC program at step 712.Indeed, since the workpiece's tooth pattern is created by the cuttingtool's geometry and the profile of the cutting tool accordinglycorresponds to the tooth pattern to be achieved, the workpiece's toothwidth can be adjusted by adjusting the radial location of the cuttingtool's profile. The cutting tool is then subjected to a new dressingoperation according to the modified NC program and the workpiecesubjected to further machining at step 416 using the redressed cuttingtool, as discussed above with reference to FIG. 5. The entire cycle ofprobing, comparing, redressing and machining the workpiece with theredressed cutting tool may then be repeated as necessary until theworkpiece's tooth width is brought within tolerance of the master gaugetooth width.

Referring back to FIG. 6c , the tooth width 514 measured on theworkpiece 504 is illustrated. It can be seen from FIG. 6c that the toothwidth 514 can be controlled by adjusting the radial offset 518, andaccordingly by adjusting the radial location of the cutting tool'sprofile. Indeed, adjusting the value of the radial offset 518 modifiesthe shift or deviation in the radial direction R(x,y) of the workpiece'stooth profile relative to the nominal tooth profile. It can be seen fromFIG. 9 that, if the radial offset is sufficiently small (e.g. when 75%of the tolerance of the engineering drawing or manufacturing operatingsheet is achieved), meaning that the deviation of the measured toothwidth from the nominal tooth width is small (i.e. within tolerance), noredressing of the cutting tool may be needed.

As shown in FIG. 9, the radial location of the cutting tool's profile,e.g. the profile of the grinding wheel 502, can be adjusted by shifting(e.g. in the X or Y direction) the driving point 902 of the cutting tool502 and subsequently redressing the cutting tool 502. The cutting tool'sdriving point 902 is illustratively defined in the NC program as a pointwhere the cutting tool 502 is controlled by the NC machine. In theillustrated embodiment, the driving point 902 is located on the gable(reference 606 in FIG. 6d ) of the cutting tool 502. It should beunderstood that the driving point 902 may alternatively be located atanother location on the cutting tool 502, as defined by a user.

FIG. 9 further illustrates the NC toolpath that the cutting tool 502takes for OD and ID dressing, with the convex curvic tooth form shown.In one embodiment, the dressing tool 904 is fixed and has a givendressing radius or edge (not shown) and the face of the cutting tool 502is moved across the dressing radius in order to create a desired profilefor the cutting tool 502. In the illustrated embodiment, one side (OD orID) of the cutting tool 502 is dressed first in a series of passes wherethe cutting tool 502 travels from an initial (e.g. “Start ID dress” or“Start OD dress”) position to a final (or “End OD and ID dress”)position and the cutting tool 502 is shifted downwards (along the Zaxis, in the direction of arrow F) after each pass. The cutting tool 502is then re-positioned to the initial position at the opposite side (ODif the ID side was dressed first) and the procedure is repeated untilboth sides of the cutting tool 502 are fully dressed with the desired(e.g. new) shape. After a number of successive dressing passes, thecutting tool 502 is then dressed from an initial tooth profile 906(referred to as “Original profile” in FIG. 9) to a final profile 908(referred to as “New profile” in FIG. 9). One side 910 of the dressingtool 904 illustratively dresses the cutting tool's ID side (e.g. theinner surface 602) while the opposite side 912 of the dressing tool 904dresses the cutting tool's OD side (e.g. the outer surface 604).

Depending on the required tool width adjustment, the driving point 902may be shifted closer to (e.g. in the direction of arrow D) or furtheraway from (e.g. in the direction of arrow E) the dressing tool 904, withthe latter remaining stationary and dressing the cutting tool 502upwards. The cutting tool's profile can then be shifted accordinglyduring the dressing cycle, as shown in FIG. 10a , FIG. 10b , FIG. 10c ,and FIG. 10b . FIG. 10a and FIG. 10b illustrate shifting the radiallocation of a convex tooth profile while FIG. 10c and Fi. 10 dillustrate shifting the radial location of a concave tooth profile.

In FIG. 10a , the driving point 902 of the convex cutting tool 502 isshifted (e.g. offset) towards the outer diameter (OD) of the cuttingtool 502 (i.e. in the direction of arrow E) during dressing. As a resultof the dressing operation performed by the dressing tool 904, a layer1002 of abrasive material is removed from the cutting tool 502 and thecutting tool's profile is modified from the initial profile 906 (drawnas the bottom solid line in FIG. 10a ) to the final profile 908 a (drawnas the top solid line in FIG. 10a resulting from removal of the abrasivelayer 1002). In particular, the profile 906 is shifted radially towardsthe inner diameter (ID) of the cutting tool 502 (i.e. in the directionof arrow 1004 a) and shifted upwards (i.e. in the direction of arrow1006 a) to achieve the profile 908 a. It can be seen that the profile908 a differs from a profile 1007 a (drawn using a dashed line on FIG.10a ) that would have been achieved after dressing if the radiallocation of the driving point 902 had not been offset. Since the cuttingtool's profile is shifted radially towards ID, the tooth width(reference 514 in FIG. 6c ) created in the workpiece (reference 504 inFIG. 6c ) with the grinding wheel 502 redressed in this manner willtherefore be thinner than the tooth width machined using the original(not redressed) grinding wheel 502.

In FIG. 10b , the driving point 902 is offset towards ID (i.e. in thedirection of arrow D) and the cutting tool's profile is thereforeshifted radially towards OD (i.e. in the direction of arrow 1004 b) andshifted upwards (i.e. in the direction of arrow 1006 b) to achieve thefinal profile 908 b (drawn as the upper solid profile line in FIG. 10b). As a result, the tooth width 514 will be wider. It can be seen thatthe profile 908 b differs from a profile 1007 b (drawn using a dashedline on FIG. 10b ) that would have been achieved after dressing if theradial location of the driving point 902 had not been offset.

In FIG. 10c , the driving point 902′ of a concave cutting tool 502′ isoffset towards OD (i.e. in the direction of arrow E) and the cuttingtool's profile is accordingly modified from the initial profile 906′(drawn as the bottom solid profile line in FIG. 10c ) to the finalprofile 908 c (drawn as the upper solid profile line in FIG. 10c ), withthe profile 906′ being shifted radially towards OD (i.e. in thedirection of arrow 1004 c) and shifted upwards (i.e. in the direction ofarrow 1006 c) to achieve the profile 908 c. As a result, the tooth width514 will be thinner. It can be seen that the profile 908 c differs froma profile 1007 c (drawn using a dashed line on FIG. 10c ) that wouldhave been achieved after dressing if the radial location of the drivingpoint 902′ had not been offset.

In FIG. 10d , the driving point 902′ is offset towards ID (i.e. in thedirection of arrow D) and the cutting tool's profile is shifted radiallytowards ID (i.e. in the direction of arrow 1004 d) and shifted upwards(i.e. in the direction of arrow 1006 d) to achieve the final profile 908d (drawn as the upper solid profile line in FIG. 10d ). As a result, thetooth width 514 will be wider. It can be seen that the profile 908 ddiffers from a profile 1007 d (drawn using a dashed line on FIG. 10d )that would have been achieved after dressing if the radial location ofthe driving point 902′ had not been offset.

Referring now to FIG. 11 and FIG. 6c , the step 418 of further machiningthe semi-finished surface to achieve the desired toothed member geometryillustratively comprises generating a machining program for bringing theheight (reference 520 in FIG. 6c ) of the workpiece's pitch plane(reference 516 in FIG. 6c ) to a nominal pitch plane height (e.g.determined from the master gauge). In order to determine the pitch planeheight 520, the semi-finished surface, particularly the top and/orbottom face of the machined workpiece, is probed at step 1102 versus areference datum (reference 522 in FIG. 6c ) that may be defined on theworkpiece or fixture. Knowing the value of the tooth depth measured onthe semi-finished workpiece (at step 412 in FIG. 5), the pitch height520 can be calculated on the basis of the acquired measurements. Adifference between the computed pitch plane height 520 and the nominalpitch plane height is then computed at step 1104. At step 1106, it isdetermined from the computed difference a distance (in the Z or “plunge”direction of FIG. 6c ) by which to further machine the workpiece untilthe pitch plane height is brought to nominal. At step 1108, the cuttingtool is then plunged into the workpiece by the distance determined atstep 1106, thereby bringing the pitch plane height to nominal andachieving the desired finished surface (i.e. the desired toothed membergeometry).

Referring now to FIG. 12, a system 1200 for machining a toothed memberwill now be described. The system 1200 comprises one or more server(s)1202. For example, a series of servers corresponding to a web server, anapplication server, and a database server may be used. These servers areall represented by server 1202 in FIG. 12. The server 1202 is incommunication over a network 1204, such as the Internet, a cellularnetwork, or others known to those skilled in the art, with a ComputerNumerical Control (CNC) machining center 1206. The CNC machining center1206 may comprise a CNC machine 1208 comprising a cutting tool (notshown) adapted to machine a workpiece (not shown) into the desiredtoothed member. The cutting tool part of the CNC machine 1208 may bedressed using a dressing tool 1210. The CNC machining center 1206 mayfurther comprise a measuring device 1212, such as a probing system (notshown) integrated with the CNC machine 1208 or a CMM (not shown). Itshould be understood that the measuring device 1212 may comprise anyother suitable part sensing system using one of a variety of contact andnon-contact technologies.

The server 1202 may comprise, amongst other things, a processor 1214coupled to a memory 1216 and having a plurality of applications 1218 a,. . . , 1218 n running thereon. The processor 1214 may access the memory1316 to retrieve data. The processor 1214 may be any device that canperform operations on data. Examples are a central processing unit(CPU), a microprocessor, and a front-end processor. The applications1218 a, . . . , 1218 n are coupled to the processor 1214 and configuredto perform various tasks as explained below in more detail. It should beunderstood that while the applications 1218 a, . . . , 12318 n presentedherein are illustrated and described as separate entities, they may becombined or separated in a variety of ways.

The memory 1216 accessible by the processor 1214 may receive and storedata. The memory 1216 may be a main memory, such as a high speed RandomAccess Memory (RAM), or an auxiliary storage unit, such as a hard diskor flash memory. The memory 1216 may be any other type of memory, suchas a Read-Only Memory (ROM), Erasable Programmable Read-Only Memory(EPROM), or optical storage media such as a videodisc and a compactdisc.

One or more databases 1220 may be integrated directly into the memory1216 or may be provided separately therefrom and remotely from theserver 1202 (as illustrated). In the case of a remote access to thedatabases 1220, access may occur via any type of network 1204, asindicated above. The databases 1220 described herein may be provided ascollections of data or information organized for rapid search andretrieval by a computer. The databases 1220 may be structured tofacilitate storage, retrieval, modification, and deletion of data inconjunction with various data-processing operations. The databases 1220may consist of a file or sets of files that can be broken down intorecords, each of which consists of one or more fields. Databaseinformation may be retrieved through queries using keywords and sortingcommands, in order to rapidly search, rearrange, group, and select thefield. The databases 1220 may be any organization of data on a datastorage medium, such as one or more servers.

In one embodiment, the databases 1220 are secure web servers andHypertext Transport Protocol Secure (HTTPS) capable of supportingTransport Layer Security (TLS), which is a protocol used for access tothe data. Communications to and from the secure web servers may besecured using Secure Sockets Layer (SSL). Identity verification of auser may be performed using usernames and passwords for all users.Various levels of access rights may be provided to multiple levels ofusers.

Alternatively, any known communication protocols that enable deviceswithin a computer network to exchange information may be used. Examplesof protocols are as follows: IP (Internet Protocol), UDP (User DatagramProtocol), TCP (Transmission Control Protocol), DHCP (Dynamic HostConfiguration Protocol), HTTP (Hypertext Transfer Protocol), FTP (FileTransfer Protocol), Telnet (Telnet Remote Protocol), SSH (Secure ShellRemote Protocol).

FIG. 13 is an exemplary embodiment of an application 1218 a running onthe processor 1214. The application 1218 a illustratively comprises areceiving module 1302, a probing and comparison module 1304, a cuttingtool redressing module 1306, a machining program module 1308, and anoutput module 1310, used to implement the methods described herein abovewith reference to FIGS. 2 to 5, FIG. 7, and FIG. 11.

The receiving module 1302 illustratively receives a signal indicatingthat a workpiece to be machined is in a loading position on the NCmachine 1208. The machining program module 1308 then generates a controlsignal (e.g. NC program) comprising instructions to cause the cuttingtool to plunge into the workpiece up to a predetermined partial depth.The control signal may be sent by the output module 1310 to the cuttingtool provided on the NC machine 1208. Once the semi-finished surface hasbeen obtained, the probing and comparison module 1304 may then output(e.g. via the output module 1310) a control signal comprisinginstructions to cause the measuring device (reference 1212 of FIG. 13)to acquire measurements (e.g. dimensions) of the semi-finished surface.The measurements may then be received at the receiving module 1302 andcompared at the probing and comparison module 1304 to nominaldimensions, which may be retrieved from the memory 1216 and/or databases1220. If the probing and comparison module 1304 determines that themeasurements are not within tolerance of the nominal measurements (ordimensions), the cutting tool redressing module 1306 may be used forgenerating and outputting to the dressing tool (reference 1210 in FIG.12) a control signal comprising instructions to cause redressing of thecutting tool in order to bring the measurements within tolerance. Afterthe cutting tool has been redressed, the machining program module 1308may generate a signal for causing further machining of the workpieceusing the redressed cutting tool. New measurements may then be acquired,as instructed by the probing and comparison module 1304, and correlatedto nominal measurements. Once the probing and comparison module 1304determines that the measurements are within tolerance of the nominaldimensions, the machining program module 1308 may then be used forgenerating and outputting to the cutting tool a control signal (e.g. NCprogram) comprising instructions to cause further machining of theworkpiece in order to achieve the finished toothed member.

It should be understood that, although the method 100 and system 1200have been described above with reference to a curvic coupling, othertoothed members may apply, as discussed above. Also, it should beunderstood that the method 100 and system 1200 may apply to other typesof engines than the one illustrated in FIG. 1. As discussed above, itshould further be understood that the method 100 and system 1200 mayapply to any suitable manufacturing process. Using the method 100 andsystem 1200, toothed members can be machined automatically and preciselyon a machine tool with little to no intervention from an operator.Automating the process in turn reduces the time required to manufacturethe parts, reduces manufacturing costs, and increases manufacturingquality and repeatability.

The above description is meant to be exemplary only, and one skilled inthe art will recognize that changes may be made to the embodimentsdescribed without departing from the scope of the invention disclosed.Modifications which fall within the scope of the present invention willbe apparent to those skilled in the art, in light of a review of thisdisclosure, and such modifications are intended to fall within theappended claims.

The invention claimed is:
 1. A method for machining from a workpiece atoothed member with a desired tooth pattern, the method comprising:machining the workpiece to a predetermined partial depth using a cuttingtool to provide a semi-finished tooth pattern created according to ageometry of the cutting tool, the predetermined partial depth less thana full depth of the desired tooth pattern; comparing computed parametersof the semi-finished tooth pattern based on dimensions of thesemi-finished tooth pattern to nominal parameters of the semi-finishedtooth pattern and determining whether the computed parameters are withina predetermined tolerance of the nominal dimensions for thesemi-finished tooth pattern at the predetermined partial depth;modifying the geometry of the cutting tool to correct deviations of thecomputed parameters from the tolerance when the computed parameters arenot within the predetermined tolerance of the nominal dimensions, andmachining the workpiece with the modified cutting tool to bring thedimensions of the semi-finished tooth pattern within the tolerance forthe semi-finished tooth pattern at the predetermined partial depth; andmachining the workpiece to the full depth to provide the desired toothpattern when the dimensions of the semi-finished tooth pattern arewithin the tolerance for the semi-finished tooth pattern at thepredetermined partial depth.
 2. The method of claim 1, wherein modifyingthe geometry of the cutting tool comprises adjusting a machining programof the cutting tool and performing a dressing operation on the cuttingtool in accordance with the adjusted machining program.
 3. The method ofclaim 1, wherein modifying the geometry of the cutting tool comprisesmodifying a pressure angle of the cutting tool.
 4. The method of claim1, wherein modifying the geometry of the cutting tool comprisesmodifying a radial distance between the cutting tool and a dressingtool.
 5. The method of claim 1, wherein modifying the geometry of thecutting tool comprises radially shifting the geometry of the cuttingtool to adjust a radial offset of the semi-finished tooth pattern. 6.The method of claim 1, further comprising probing the workpiece at aplurality of locations of the semi-finished pattern to obtain thedimensions of the semi-finished tooth pattern.
 7. The method of claim 6,wherein probing the workpiece comprises probing one of an upper and alower face of the semi-finished pattern relative to a reference datumand computing a pitch plane height for the semi-finished tooth pattern.8. The method of claim 7, wherein machining the workpiece to the fulldepth comprises computing a distance equal to a difference between thecomputed pitch plane height and a nominal pitch plane height andplunging the cutting tool into the workpiece by the distance.
 9. Themethod of claim 1, further comprising computing a tooth depth, a toothwidth, and a pressure angle for the semi-finished tooth pattern as thecomputed parameters.
 10. The method of claim 1, wherein the nominaldimensions are obtained from a virtual tooth pattern.
 11. The method ofclaim 10, wherein the virtual tooth pattern is obtained by scanningsurfaces of a master gauge, the virtual tooth pattern complementary tothe desired tooth pattern.